application today [1-3]. Some advantages of using VFDs are: higher efficiency of a driven motor, fast control response, accurate speed control, good torque response, etc. [4, 5]. High switching frequency of VFD in correlation with the high rate of voltage rise and fall times (50-300ns [6-9]), sets a significant voltage stress on the winding insulation system. Winding insulation system, together with two conductive parts of the machine, forms a capacitive coupling. Inside an EM, the following capacitive couplings can be observed, as shown in Fig. 1 [10]:
At low frequencies, mentioned capacitive couplings can be neglected, considering their very low value (i.e. order of tenths of pF [11] up to tenths of nF [12, 13]). However, the effect of these couplings becomes apparent in inverterdriven EM due to the high frequency (HF) switched voltages. The resulting effects are conducted and radiated electromagnetic interference (EMI). The radiated EMI, found in the 30MHz-40GHz frequency range, will not be addressed in this paper [14]. The conducted EMI, however, is manifested through differential- and common-mode voltages and currents (DMV, DMC, CMV and CMC, respectively) with harmonic frequencies ranging from lS0kHz up to 30MHz [lS-17]. Electronic switching elements inside an inverter, i.e. IGBTs, represent the source of this unwanted EMI. The differential-mode noise is also referred as symmetrical noise or line-to-line noise. DMC flows through one phase and returns through the other (lineto-line path). Common-mode noise is referred as asymmetrical noise or line-to-ground noise. CMC flows through all phase conductors and returns via the ground conductor. Differential- and common-mode paths are presented in Fig. 2. Connections between the phase conductors and the ground conductor are realized via (parasitic) capacitive couplings between the phase windings and the ground (i.e. stator and/or rotor core).
Unlike grid supplied machines, pulse-width modulation (PWM) inverter-fed machines inherently result in CMV on the connection point of the machine phase windings, which has a value at any point in the time as shown in the example given in Fig. 3 [18-20]. In Fig. 3a reference voltage signals are presented with red, green and blue sinusoidal signals, while triangle carrier signal is marked black. In diagrams in Figs. 3b-3d, red, green and blue rectangular signals, respectively, represent output signals of the inverter. These are also signals at the machine's input. The diagram in Fig. 3e presents the CMV signal at the machine's neutral point in respect to ground. The frequency of CMV is three times higher than the switching frequency of the inverter's IGBTs [21,22].
Above mentioned parasitic effects can cause premature failure of the electrical insulation and bearings [23, 24]. Further, equipment connected to the EM shaft (e.g. gearboxes, cooling systems) can be affected by shaft-toground capacitive currents, possibly leading to damage. To
Fig. 2: Differential and common mode paths in VFD
Differential mode path
parasitic motor/ cable capacitance
a) Triangle and reference voltage signals'" PWM signals (u,v.w) 1 o ... .. . . . . . .
-1 3.5 4 4.5 5 5.5 b) PWM signal (u)
200 100
3.5 4 4.5 5.5 c) PWM signal (v) 200 IF' .. .
����lW' I tl U 100 o 3.5 4 4.5 5 5.5 d) PWM signal (w)
:� tI I U l llill llll,l l l __ U U 5 U 6 e) Common-Mode voltage
200 . . . . . : . . .
. . . . . .
100 ' . . . . . . . . . . . . . . . . .
o .. . . . . . . . ,
U 4 U 5 U 6
Fig. 3: PWM signals; a) sinusoidal reference voltage signals and the carrier signal; b) PWM signal of first phase; c) PWM signal of second phase; d) PWM signal of third phase; e) CMV signal at the neutral point in reference to the ground [20]
prevent mentioned damage, one must minimize the capacitive couplings. However, in order to analyze parasitic capacitive couplings at HFs, equivalent circuit of a winding and a coil at HF as in Section 3 must be observed [2S-32]. This paper presents an overview of the most common and applied analytical methods for calculation of the parasitic capacitances of different types of windings which are given in Section 4 [2S-46]. Parasitic capacitive couplings in the bearings and between stator and rotor core will not be addressed in this paper.
II. WHY MINIMIZING THE CAPACITIVE COUPLING?
For EMs, which are working with SOHz or 60Hz nominal frequency, the insulation system of the windings is usually designed according to the EM manufacturer's best practice and experience and based on general standards and latest technologies. Even for inverter-fed EM with nominal frequency e.g. 400Hz, the insulation system will often be the same as for SO/60Hz or enhanced by applying different insulating material of more insulation layers. In order to demonstrate the necessity of minimizing the capacitive couplings of the insulation system, an example given in table 1 shows what happens with the capacitive reactance of the insulation in the case of different frequencies. For this example assumed capacitance of the winding insulation system is SnF and SpF.
TABLE 1: EXAMPLE OF INSULATION CAPACITIVE REACTANCE
AT DIFFERENT FREQUENCIES
1[Hz] 50 400 150k 30M
C�5nF 636.6k 79.6k 212.2 1.1 1
Xc = -;;;:c [ill C�5pF 636.6M 79.6M 212.2k I.Ik
From this example it can be seen that at 50Hz and even at 400Hz the reactance is still high. However, considering the HF harmonics of CM signals, it is obvious that reactance is almost negligible. It should be noted that this example is only given for the capacitive reactance, while in reality, the total impedance of the winding insulation system should be considered. This impedance can be calculated using the equivalent circuits given in Section 3 or measured with appropriate high current RLC meters.
III. HIGH-FREQUENCY MODEL OF THE WINDING
Referenced publications propose lumped parameter circuit models in order to qualify and quantify parasitic capacitances of windings. To analyze the winding and its insulation system at HF of CM signals, the basic lumped parameter equivalent circuit of a phase winding at HF should be observed as in Fig. 4 [25-27]. Here: L is the total inductance and it includes main and leakage inductances, R is the serial connection of ac winding resistance and core resistance, C represents stray capacitance which consists of turn-to-turn and turn-to-ground capacitances, which will be further elaborated on in Section 4. Inductance and resistance are frequency dependent, due to eddy-currents in the core, and skin and proximity effect in the winding. Stray capacitance is assumed not to be frequency dependent [29].
In a more detailed representation, equivalent circuits of a coil are given in Figs. 5 and 6 [30] and [32]. Some authors are applying the same equivalent circuits to represent the winding [31]. These equivalent circuits represent a coil and designations are: Rp/ represents AC iron losses (eddycurrent and hysteresis losses inside the magnetic core and the frame); RCI represents dissipative phenomena due to HF capacitive current and dielectric losses; RLJ is AC wire resistance; CJ represents turn-to-turn capacitance; LJ is overall inductance of the coil (sum of overhang part and slot part of the coil). Overall inductance LJ and AC wire resistance are frequency dependent, but in order to use this equivalent circuit in frequency and time domain, these values are usually set to average value [11]. Values of Rp/, RCI and RLJ are usually a couple of kQ-:-10x kQ, 10x Q and 100x Q, respectively. Additional capacitance towards the ground must be taken into consideration with the resistance Rg and the capacitance Cg.
Fig. 4: The basic lumped parameter equivalent circuit of a phase winding in HF domain
Rp1
A B
Fig. 5: Detailed equivalent circuit of a coil at HF
A
Fig. 6: Detailed equivalent circuit of coil at HF with capacitance towards the ground being taken into consideration
IV. TYPES OF CAPAC IT ANCES
Basic types of parasitic capacitances regarding the windings are turn-to-turn and turn-to-ground. Additionally, coil-to-coil, coil-to-ground, phase-to-phase, and phase-to-ground capacitances can be observed as an extension of basic types [47].
From the two basic types of capacitances, the capacitance matrix [48,49] can be formed with diagonal elements Cu, which are called "self-capacitance coefficients" [49-55]. They are positive constants and represent, the sum of c�racitances �etween the i1h conductor and every other Ut ) conductor III the system, as well as between the ith conductor and its ground. Nondiagonal elements Cij, which are called "mutualcapacitance coefficients", and exist between the ith and lh conductor. They are negative constants that represent the mutual partial capacitance between the ith and /h conductor in the system. In Fig. 7, an example of a random coil crosssection with four conductors is given.
Fig. 7: An example of capacitances between four conductors of which two have round and two have rectangular cross-section [54]
The combination of cross-sections of the conductors (two rectangular and two round conductors) is given deliberately. The capacitance matrix for this example is given with (1). For the general case, this matrix would be given with (2).
c:; I +C:;2 + +C:;3+C:;4
-C:; I
C;1+C;2+ (1)
+C;3+C;4 -C;4
-CI3 �1+�2+ +�3+C44
-e:;2 -e:; ll
C21+�2+ -�n +,,+C2J1 (2)
-c'12 Cnl +c'12 + +···+c'm
A. Turn-to-Turn Capacitance Turn-to-turn capacitance implies the capacitance
between any two conductors inside the same coil. Turn-toturn capacitance Cit is calculated between the turns i andj Utj). This capacitance can be calculated in different ways, depending on the shape of the conductor and their arrangement in the slot.
J) Formed winding - Conductors with rectangular crosssection: For rectangular conductors it is relatively easy to calculate Cit. Thanks to the surface contours of formwound coils, which are sufficiently and necessarily regular to permit the representation of a coil in a slot or end region by equivalent parallel-plate capacitors [33]. In this case, capacitance is given with (3), where E:, A, and de, are permittivity, conductor surface and distance between two turns edges, respectively [34].
A ett = E·(i
e (3)
Figs. 8-10 present turn-to-turn capacitance for simple, two-turn coil, and one-layer and two-layer multi-turn coils. In the case as in Fig. 10, turn-to-turn capacitance will be different due to different surfaces between two adjacent turns (CttdCtt2).
Taking into account parallel plate capacitor, another approach for calculation of turn-to-turn capacitance is given in [28] and with regard to the Fig. 11. It is based on the calculation of the capacitance between two infinite, straight, parallel conductors in homogenous medium (in this case it will be assumed air).
Fig. 8: Simple, two-turn coil and its capacitances [33]
CIgl
� rI Ctt
8 Ctt
CIg2
I---I Ctt
CIg2 r-I Ctt
� Ctt
CIgl
Ctt
Fig. 9: Single-row coil and distributed network of its capacitances [33]
Clgl Clll
..L II I lc1I2 1� CIg2
TC'12 Clll ICII2 CIg2
t--I+---III I I ICI12 Clll.I CII2 CIg2
I--I�-II I I TCII2 Clll T CII2 CIg2
I----�+----III � I ICII21 1 TCtt21
Clll Clgl
Fig. 10: Double-row coil and distributed network of its capacitances [33]
DI12
h
Fig. 11: Cross-section of rectangular wires and ground [28]
Turn-to-turn capacitance from Fig. 11 would be:
k ED L b (4) C tt = -d--=---a-
The factor k includes edge effects which are the function of the winding geometry. Equation (4) does not consider insulation coating thickness, i.e. t« d-a. If the insulation coating thickness cannot be neglected, the equation (5) should be used.
k ED L b Ctt = --------:;--
d - a - 2 . t . ( 1 - E�) (5)
In equations (4) and (5) it is assumed that L is the turn length.
2) Formed winding - Conductors with round cross-section: In the case of two conductors with round cross-section in homogenous medium of permittivity E:, capacitance between them, according to [14] and [35], can be calculated as:
1[ EL Ctt = (6)
cosh-1 (�)
Where L is the length of a conductor (turn), distance between centers of the two conductors is d, while D represents the diameter of these conductors. In the case of diD> 3, mentioned capacitance reduces to:
1[ EL Ctt =
In (2 .�) (7)
In another approach, similar to the case of the rectangular wire from Fig. 11, capacitance between two turns can be calculated on the basis of the calculation of infinite, parallel conductors with round cross-section in homogenous medium as presented in Fig. 12 [28]. The calculation neglecting the insulation thickness is given by:
(8)
DI12
h
d r I t
� e-O Fig. 12: Cross-section of round wires and ground, D=2r [28]
Equation (8) is the same as (6) with regards to the mathematical identity between cosh-I(x) and In(x). If insulation thickness cannot be neglected, it should be taken into consideration by applying of the following equation:
Where factor F is given by:
F _ dlz r - 1 (l_f)l-ET
Derivation of (9) is presented in detail in [28].
(9)
(10)
Main downside of the previous two methods described with equations (6)-(9) is the limitation to single-layer coils. Further, these two methods include only the capacitance calculated in regards to the shortest possible path along the center axis of two turns, i.e. axis which connects the centers of two observed turns (conservative approximation). The actual capacitance between two conductors will vary due to the roundness of the conductors, which means that the lines of the electric field will not have an equal length. In order to obtain a result which can be applied to a multi-layer coil, and to take into consideration different length paths between two conductors as given in Fig. 13, previous equations must be expanded.
The equivalent capacitance consists of three capacitances connected in series - capacitance of the insulation layer of the first turn, capacitance of the air gap between two turns, and capacitance of the second turn [36]. From Fig. 13 it can be seen that a basic cell for capacitance calculation can be extracted in regards to the symmetry as according to Fig. 14.
Further, from the geometrical symmetry of the coil and with the assumption that the turn in the middle is fully surrounded with other turns, a turn can be divided into elementary surfaces which face adjacent turn. The angle between two elementary cylindrical surfaces of adjacent turns covers 1[/3. Turns located at the edges of a coil differ
Fig. 13: Hexagonal arrangement of conductors in a multi-layer winding [36]
Fig. 14: A basic cell for the calculation of CII [36]
from this model, but in order to make a first-order approximation, all turns will be considered in accordance to this basic cell. This approximation is equal to neglecting the fringing effects. In the zone of 1[/3, the air gap path between two elementary cylindrical surfaces of adjacent turns is the length of a line of the electric field connecting the two opposite elementary cylindrical surfaces, i.e. x. This length is a function of angle B, as shown in Fig. 15. In this region the capacitance must be integrated along the angle B, i.e. over the angle of 1[/3. The elementary cylindrical surface for calculating the insulation layer capacitance is given in Fig. 16.
First, the capacitance of the insulating coating is calculated with respect to Fig. 16. The elementary capacitance of the cylindrical insulation coating shell is given by:
dC = Co cr dl dB c dr
(11)
Fig. 15: Assumed path of an electric field line between two adjacent turns for calculating CII [36]
Fig. 16: The elementary cylindrical surface of an insulation coating [36]
The result of the equation (11) after the integration over the turn length L and insulation thickness t, will be:
dCc = Co cr L de
In Do (12) Dc
The capacitance of the air gap is calculated considering the assumed paths as a function of B. The paths are given by:
xCB) = DoC1 - cos B) (13)
And the air gap capacitance is:
Co L dCg =
2C1 _ cos B) de (14)
The total capacitance between two turns is: dCc dCg
dCtt = dCc + 2 dCg
(15)
After the integration over the angle of 1[/3:
(16)
where:
M=-l+v'3 (17)
and
N = 2Er + In Do . Dc (18)
In order to simplify equation (16), instead of e, a new angle e* is introduced. It is the angle at which the serial connection of elementary capacitances of the insulation coatings is equal to the elementary capacitance of the air gap, i.e.:
dC e* � T = dCg (19)
The capacitance of the insulating coating is now: 2 Eo Er L e*
Cc = D (20) In-2.. Dc
If it is assumed that the insulation coating thickness s is small comparing to the conductor diameter, cylindrical shell can be further approximated with parallel plate capacitor, so (20) becomes:
Cc = Eo Er L Da e*
(21) t
And the air gap capacitance will be:
Cg = Eo L [cot (�*) - cot (�)]
(22)
Where Da represents average diameter of the insulation coating:
(23)
With a couple of simple mathematical operations between (12), (14) (19), (20) and (21), angle e* can be expressed as:
e* = cos-1 (1 -�) Er Da
(24)
Finally, the overall turn-to turn capacitance will be: E D e* e'
Ctt = Eo L [r t + cot ( "2 ) - 3.732] (25)
Previous analysis is given under the assumption of uniformly-wound single-wire coils.
Detailed derivation of (25) is presented in [37].
3) Random winding (mush-wound cois) - Conductors with round cross-section: Random-wound coils imply bundle of round wires inserted into the slot, neglecting the order of the wires [38, 39]. This type of winding is used in lowvoltage machines (up to lkV). Due to the randomly inserted wire, it can happen that the first turn can be next to the last one, and in that case the voltage difference between these two turns is the highest. Not knowing the actual wire distribution inside the slot, it is impossible to
calculate the turn-to-turn capacitance based on the coil geometry. The turn-to-turn capacitance can be obtained only by measurements and then calculating the capacitance via resonant frequency and inductance matrix as explained in [29] and [32], or via stored energy as presented in [40,41].
B. Turn-to-Ground Capacitance Turn-to-ground capacitances (Cg) is the capacitance
between the turn and the slot wall. It is also referred as a turn self-capacitance. It is larger than turn-to-turn capacitance and it can also be calculated in different ways, depending on the wire type and its configuration in the slot.
J) Formed winding - Conductors with rectangular crosssection: From Figs. 8-10 it can be noticed that Cg will be the same for two-turn coil, but it will be different in the case of multi-turn coils. The difference will appear between the outer turns (top and bottom) and the inner turns, which will have the capacitance CgJ and Ctg2, respectively (Ctg4Cg2). This difference appears due to difference of surfaces which are facing the slot wall. It is obvious that Cg, > Cg2 considering that the outer turn has larger surface.
Turn-to-ground capacitance for the coil in Fig. 11 can be calculated in the similar way as Cu. If the insulation coating thickness is negligible, i.e. t« d,-a/2, the result will be:
kED L b Ctg = a
h-Z (26)
If the insulation coating thickness cannot be neglected, Cg will be:
kED L b Ctg = 1
h-!!:'-t (l--) 2 Er
(27)
2) Formed winding - Conductors with round cross-section: For the case from Fig. 12, Ctg will be given by (28) if the insulation coating thickness can be neglected, i.e. t« h-r, if that is not the case, then expression (29) is applied.
2 1[ Eo L (28)
(29)
Where factor F' is given by:
(30)
To calculate turn-to-ground capacitance for a multilayer coil from Fig. 13, similar methodology will be applied as for Cu. If it would be assumed that the slot wall is the symmetry plane from Fig. 15, the path lengths of the electric field lines between the tum and the slot wall will be a half of the path lengths between two turns. This means that Ctg will be a serial connection of the coating capacitance given by (12) and a half of the air capacitance given by (14), as shown in Fig. 17. After solving a simple network of serial capacitances it can be obtained that Cg is double the Cu given by (25), i.e.:
(31)
In the reality, the basic cell for calculating Cg is wider than the one used for calculating Cu. The angle between the elementary cylindrical surfaces from Fig. 15 and the ground plane will actually be n/2. For the simplicity reasons, ex pression (31) is gi ven as a first-order approximation.
3) Random winding (mush-wound cois) - Conductors with round cross-section: As explained in the case of Cu, for random-wound coil it is not possible to determine Cg on the basis of coil geometry. In [42] Cg was determined as an average value of the measured coil-to-ground capacitances, divided with the number of turns. It can be stated that turn-to-ground capacitance can be obtained only by measurements [32] and [42].
C. Layer-to-Layer and Layer-to-Ground
In the previous interpretation of turn-to-turn and turnto-ground capacitance it was explained how to calculate mentioned capacitance, considering them as an elementary capacitances regarding the windings in EM. The next step
Fig. 17: Assumed path of the electric field line between two adjacent turns for calculating etg [36]
would be to consider layer-to-layer CII and layer-to-ground Cig capacitances. As above-mentioned, coils, i.e. windings can be single- or multi-layer. For a single-layer coil (winding) CII does not exist, while Cig can be observed through the equivalent II circuit as in [27] by solving the network of distributed capacitances by applying D-Y transformation for capacitances. In the case of multi-layer coils, CII and Cig can be calculated according to [43], which suggests to observe a layer as plate:
bw l Clx = 5 (32)
e Where x in the subscript stands for I - layer or g -
ground. In the expression blV, I and Se represent coil width, an average length of a tum, and the distance between horizontal axis of a layer, respectively. For Cll, Se is calculated as:
Se = boll + 1.26 Do - 1.15 Dc
While for CIg, Se is:
1 Se = bolg +"2 (1.26 Do - 1.15 DJ
(33)
(34)
Distance between two layers, i.e. between a layer and ground is given with All, i.e. Aig.
Alternative expression for calculating CII is presented in [44]:
nt (nt + 1) (2 nt + 1) Cll =
6 2 l Ctt (35) nt
where nt is number of turns in the layer and I is average length of a tum.
Voltage distribution among layers must be taken into consideration as well, as shown in [43,44].
If z represents the number of layers in a coil then selfcapacitance of a coil is given as:
(36)
D. Coil-to-Coil and Coil-to-Ground
Depending on the form of a coil (rectangular or round), coil-to-coil capacitance Ccc and coil-to-ground Ccg can be approximated with the expressions for a parallel plate capacitor or round conductor [43-45].
E. Phase-to-Phase and Phase-to-Ground
The phase-to-phase capacitances Cpp are formed mainly by the winding parts of the different phases U, V and W, in the winding overhang and inside the slots [21]. This type of capacitance is usually an order of magnitude smaller than phase-to-ground capacitance [21] and [31]. This difference is attributed to the different parts of a
machine that form the capacitances. The stator windings are embedded into the stator slots of the stator core iron stack where the area of contact is large and the distance is small when compared with the area and the distance between the phases in the winding overhang.
The stator phase-to-ground capacitance epg can be approximated as a Qsl3 parallel plate capacitor, where Qs is a number of stator slots [21] and [46].
V. DISCUSSION AND RECOMMENDA nONS
Many assumptions and approximations are applied in order to simplify the calculations of a winding parasitic capacitive couplings. Further, the comparison of results obtained by analytical methods and measurements done in referenced publications report a deviation of 20% [21-37] up to even 174% [21]. Thus, authors of mentioned publications are proposing correction coefficients.
The authors of this article would suggest following recommendations to be taken in account when determining the parasitic capacitances in EM:
• details of design of EM should be known before proceeding with the parasitic capacitance calculation. These details imply the knowledge of the complete insulation system applied, number and shape of the wire used, the number of slots and their shape, etc.
• capacitances between non-adjacent turns, and between non-adjacent layers should not be neglected.
• finite elements (FE) based calculations in combination with analytical analysis presented in this paper, should be used in order to determine parasitic capacitances with increased accuracy.
• measurements on EMs should be done without the rotor in place, in order to avoid stator winding-torotor capacitance and bearing capacitance - in that way only turn-to-turn capacitance and turn-to-ground capacitance are considered.
• voltage distribution along the coil must be considered when designing a coil. In order to minimize the capacitance, layers in a coil should be wound in the same direction. This, however demands longer connection between adjacent layers, thus it presents a trade-off between more active material for the coil production and minimizing the capacitances.
• dynamic effects, such as the influence of proximity effects that can lead to inductance variations within the coil should be considered.
VI. CONCLUSION
Various analytical methods for the calculation of the parasitic capacitive couplings in regards to a winding are
presented in this paper. As such, many simplifications have been applied in order to obtain the presented equations. However, it can be concluded that truly accurate results can only be obtained by applying accurate analytical or FE based calculations and considering the real configuration of the winding in parallel with measurements. Future work will be focused on deriving the complete parasitic capacitance matrix based on analytical and FE models in order to implement improved HF model in EMs. Such improved model can then be used during the EM design process in order to minimize the effects of EMI.
ACKNOWLEDGMENT
This paper is part of the ADvanced Electric Powertrain Technology (ADEPT) project which is an EU funded Marie Curie ITN project, grant number 607361. Within ADEPT a virtual and hardware tool are created to assist the design and analysis of future electric propulsions. Especially within the context of the paradigm shift from fuel powered combustion engines to alternative energy sources (e.g. fuel cells, solar cells, and batteries) in vehicles like motorbikes, cars, trucks, boats, planes. The design of these high performance, low cost and clean propulsion systems has stipulated an international cooperation of multiple disciplines such as physics, mathematics, electrical engineering, mechanical engineering and specialisms like control engineering and safety. By cooperation of these disciplines in a structured way, the ADEPT program provides a virtual research lab community from labs of European universities and industries [56].
REFERENCES
[1] A. Hughes and B. Drury, Electric Motors and Drives -Fundamentals, Types and Applications, 4th ed., Elsevier Ltd., USA, 2013
[2] N. Mohan, Electric Drives - An Integrative Approach, MNPERE, USA, 2003
[4] ABB drives, Technical guide No.1 - Direct torque control-the world's most advanced AC drive technology, Rev.C, ABB, 2011
[5] K. Shirabe, M. Swamy, J. Kang, M. Hisatsune, Y. Wu, D. Kebort and J. Honoa, Advantages ojHigh Frequency PWM in AC Motor Drive Applications, IEEE Energy Conversion Congress and Exposition (ECCE), USA, Releigh, 2012
[10] J.Adabi, F.Zare, G.Ledwich, A.Ghosh and R. D. Lorenz, Bearing Damage Analysis by Calculation ojCapacitive Coupling between Inner and Outer Races oj a Ball, IEEE 13th Conference on Power
Electronics and Motion Control (EPE-PEMC 2008), Poznan, Poland, pp.903-907, September 2008
[11] L. Arnedo and K. Venkatesan, High Frequency Modeling of Induction Motor Drives for EMI and Overvoltage Mitigation Studies, IEEE International Conference on Electric Machines and Drives (lEMDC'03), VoLl ,pp. 468 - 474, June 2003
[12] B. Mirafzal, G. L. Skibinski and R. M. Tallam, Determination of Parameters in the Universal Induction Motor Model, IEEE Transactions on Industry Applications, Vol. 45, No. 1, pp. 142-151, January/February 2009
[13] A. Boglietti, A. Cavagnino and M. Lazzari, Experimental HighFrequency Parameter Identification of AC Electrical Motors, IEEE Transactions on Industry Applications, Vol. 43, No. 1, January/February 2007
[14] H. W. Ott, Electromagnetic Compatibility Engineering, John Wiley and Sons, Inc., USA, 2009
[15] M. Berman, All about EMI filters, TDK-Lambda Americas, www.us.tdk-lambda.com!lp.San Diego.CA. October 2008.
[16] EN 55022, "Information technology equipment - Radio disturbance characteristics Limits and methods of measurement," CENELEC, September 2006
[17] T. Williams, EMC for Product Designers, 4th ed. pp. 77, Newnes, USA,2006
[18] S. Ogasawara and H. Akagi, Modeling and Damping of HighFrequency Leakage Currents in PWM Inverter-Fed AC Motor Drive Systems, IEEE Transactions on Industry Applications, Vol. 32, No. 5, pp. 1105-1114, September/October 1996
[19] B. Muralidhara, A. Ramachandran, R. Srinivasan and M. C. Reddy, Experimental Measurement of Shaft Voltage and Bearing Current in an Inverter Fed Three Phase Induction Motor Drive, In the Proc. of the 3rd International Conference on Electronics Computer Technology (lCECT), Vo1.2, pp.37-41, April 2011
[20] F. Abdallah and M. Alakiila, Capacitively Coupled Transmission Line Model and Validation of a Winding-an-Core Prototype, In the Proc. of the International Symposium on Electromagnetic Compatibility (EMC Europe 2013), Brugge, Belgium, September 2013
[21] A. Muetze, Bearing currents in Inverter-Fed AC-Motors, PhD thesis, Elektrotechnik und Informationstechnik der Technischen Universitaet Darmstadt, Germany, January 2004
[22] BALDOR, Shaft Voltage and Bearing Current, A technical white paper, BALDOR Electric Company, 20
[23] S. Chen and T.A. Lipo, Bearing Currents and Shaft Voltages of an Induction Motor Under Hard- and Soft-Switching Inverter Excitation, IEEE Transactions on Industry Applications, Vol. 34, No. 5, pp. 1042-1048, September/October 1998
[24] S. Bhattacharya, L. Resta, D.M. Divan and D.W. Novotny, Experimental Comparison of Motor Bearing Currents with PWM Hard- and Soft-Switched Voltage-Source Inverters, IEEE Transactions on Power Electronics, Vol. 14, No. 3, pp. 552-562, May 1999
[25] J. Luszcz and I. Moson, AC Motor Windings Circuit Model for Common Mode EMI Current Analysis, In the Proc. of the 5th International Conference-Workshop on Compatibility in Power Electronics (CPE '07), 2007
[26] A. Massarini and M. K. Kazimierczuk, Self-Capacitance of Inductors, IEEE Transactions on Power Electronics, Vol. 12, No. 4, pp. 671-676, July 1997
[27] G. Grandi, M. K. Kazimierczuk, A. Massarini and U. Reggiani, Stray Capacitances of Single-Layer Solenoid Air-Core Inductors, IEEE Transactions on Industry Applications, Vol. 35, No. 5, pp. 1162-1168, September/October 1999
[28] G. Grandi, M. K. Kazimierczuk, A. Massarini and U. Reggiani, Stray Capacitances of Single-Layer Air-Core Inductors for High
Frequency Applications, IEEE Transactions on Industry Applications, Vol. 3, pp. 1384-1388, October 1996
[29] G. Grandi, M. K. Kazimierczuk, A. Massarini, U. Reggiani and G. Sancineto, Model of Laminated Iron-Core Inductors for High Frequencies, IEEE Transactions on Magnetics, Vol. 40, No. 4, pp. 1839-1845, July 2004
[30] G. Grandi, D. Casadei and A. Massarini, High Frequency Lumped Parameter Model for AC Motor Windings, In the Proc. of the European Conference on Power Electronics and Applications (EPE '97), vol.2, pp. 2578-2583, Trondheim, Norway, 1997
[31] C. Martis, H. Hedesiu, B. Tataranu, High-Frequency Model and Conductive Interferences of a Small Doubly Salient Permanent Magnet Machine, IEEE International Conference on Industrial technology (ICIT), Vo1.3, pp. 1378-1383, Hammamet, Tunisia, December 2004
[32] G. Grandi, D. Casadei and U. Reggini, Equivalent Circuit of Mush Wound AC Windings for High Frequency Analysis, in Proc. ISlE Conf., VoLl, pp. SS201-SS206, Guimaraes, Portugal, July 1997
[33] M. T. Wright, S. J. Yang, and K. McLeay, General theory of fastfronted Interturn Voltage Distribution in Electrical Machine Windings, , In the Proc. of the Electric Power Applications, Vo1.130, pp. 245-256, July 1983
[34] D. H. Staelin, Electromagnetics and applications, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA, 2011
[35] W. H. Hayt Jr. and J. A. Buck, Engineering Electromagnetics, 6th ed., McGraw-Hili, USA, 2001.
[36] A. Massarini, M. K. Kazimierczuk and G. Grandi, Lumped Parameter Models for Single- and Multiple-Layer Inductors, Power Electronics Specialists Conference, (PESC '96), 27th Annual IEEE, Vol. 1, pp. 295-301, Jun 1996
[37] A. Massarini and M. K. Kazimierczuk, Modeling the Parasitic Capacitance of the Inductors, In the Proc. of 16th Capacitor and Resistor Technology Symposium (CARTS 96), New Orleans, pp. 78-85, March 1996
[38] J. Pyrhbnen, T. Jokinen and V. Hrabovcova, Design of Rotating Electrical Machines, 1st ed., John Wiley and Sons, Inc., USA, 2008
[39] I. Boldea and S. A. Nasar, The Induction Machines Design Handbook, 2nd ed., CRC Press, Taylor & Francis Group, USA, 2010
[40] L. Junfeng, L. Ruifang, Z. Bohua and Z. Yihuang, The Effects of End Part of Winding on Parasitic Capacitances of Induction Motor Fed by PWM Inverter, In the Proc. of 15th International Conference on Electrical Machines and Systems (lCEMS), pp. 1-5, October 2012
[41] O. Magdun, A. Binder, C. Purcarea and A. Rocks, HighFrequency Induction Machine Models for Calculation and Prediction of Common Mode Stator Ground Currents in Electric Drive Systems, In the Proc. of 13th European Conference on Power Electronics and Applications (EPE '09), pp. 1-8, September 2009
[42] L. Gubbala, A. von Jouanne, P. Enjeti, C. Singh and H. Toliyat, Voltage Distribution in the Windings of an AC Motor Subjected to High dvldt PWM Voltages, In the Proc. of 26th Annual IEEE Conference of Power Electronics Specialists (PESC '95), pp. 579-585, Vol. 1, Atlanta, USA, Jun 1995
[43] E. C. Snelling, Soft Ferrites, Properties and Application, ILIFFE Books Ltd, London, 1969
[44] L. Dalessandro, F. de Silveira Cavalcante, J. W. Kolar, SelfCapacitance of High-Voltage Transformers IEEE Transactions on Power Electronics, Vol. 22, no. 5, pp. 2081-2092, September 2007
[45] C. S. Chaves, J. R. Camacho, H. de Paula, M. L. R. Chaves and E. Saraiva, Capacitances Calculation Using FEM for Transi Overvoltage and Common Mode Currents Prediction in Inverter-
[46]
[47]
Driven Induction Motors, In the Proc. of PowerTech Conference, Trondheim, Norway, pp. 1-7, June 2011
D. Busse, J. Erdman, R. J. Kerkman, D. Schlegel and G. Skibinski, System Electrical Parameters and Their E.f[ects on Bearing Currents, IEEE Transactions on Industry ApplicatIOns, Vol. 33, No. 2, pp. 557-584, March/April 1997
H. K.Yun et aI., A Study on Inverter and Motor Winding for Conducted EMi Prediction, In the Proc. of ISlE 2001 (IEEE on Industrial Electronics), Pusan, South Korea, Vol. 2, pp. 752-758, Jun 2001
[48] A. E. Ruehli, Advances in CAD for VLSI - Circuit Analysis, Simulation and Design, Vol.3, Part 2, ElsevIer SCIence PublIshers B.V, The Netherlands, 1987
[49] V. Venegas, E. Melgoza, 1. L. Guardado, R. Mota and R. Escarela, A Time-Domain Rotating Machine Model for Switching Overvoltage Studies using Network Synthesis for the Winding Impedance, IEEE Internationl Conference on Electnc Machmes and Drives, pp. 1453-1458, San Antonio, USA, May 2005
[50] F. Abdallah, EMC Analysis of Electric Drives, Licentiate Dissertation, Faculty of Engineering, Tryckeriet i E-huset, Lund University, Lund, Sweden, 2012
[51] C. R. Paul, introduction to Electromagnetic Compatibility, 2nd
ed., John Wiley and Sons, Inc., USA, 2006.
[52] D. M. Pozar, Microwave Engineering. 3rd ed., John Wiley and Sons, Inc., USA, 2005.
[53] D. K. Cheng, Field and Wave Electromagnetics. 2nd ed., AddisonWesley series in electrical engineering, Addison-Wesley, USA, January 1989
[54] E. Di Lorenzo, The Maxwell Capacitance Matrix, White paper, WPI10301, March 2011
[55] T. Li, 3D Capacitance Extraction with the Method of Moment,
[56] Thesis, Worcester Polytechnic Institute, Worcester, Massachusetts, 201 0
A. Stefanskyi, A. Dziechciarz, F. Chauvicourt, G. E. Sfakianakis, K. Ramakrishnan, K. Niyomsatian, M. Curti, N. Djukic, P. Romanazzi, S. Ayat, S. Wiedemann, W. Peng, S. Stipetic, "Researchers within the EU funded Marie Curie ITN project ADEPT, grant number 607361 ", 2013-2017.
